It appears that is very similar to the same construction as a belted or bias ply tire of the period with layers of rubber and woven nylon fabric intermixed.
Would not thing that a tire product would help the brittleness - many of them do just the opposite. Might try Zymol's weather strip rejuvenate (or a title like that) I've used the stuff for a couple of years (though they can't legally get it any longer in this great state
put the part in a zip lock bag, add a little liquid, seal the bag, rub it around and let it sit for a week (rubbing it in again and again over the period)
Made from a number of natural oils (hands smell like your using a coconut hand cream) and originally designed to bring back old Porche door and trunk weatherstripping